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The purpose of this paper is to demonstrate new properties of continuous‐ and discrete‐time dynamical systems.

First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown.

The main result of the paper is a new theorem regarding new properties of continuous‐ and discrete‐time dynamical systems.

The present study provides a starting point for further research on the differences between continuous‐ and discrete‐time dynamical systems. This work builds on the definition of spatial symmetry.

The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous‐time dynamical systems by discrete‐time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise.

This paper offers contributions to the broader discussion of differences between continuous‐ and discrete‐time dynamical systems. In particular, the paper supports the statement that many discrete‐time processes cannot be embedded into continuous ones.

This study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.

This paper proposes an optimal method for the identification of MISO CT hybrid “Box–Jenkins” systems with unknown time delays by using the two-stage recursive least-square (TS-RLS) identification algorithm.

The effectiveness of the proposed scheme is shown with application to a simulation example.

A two-stage recursive least-square identification method is developed for multiple input single output continuous time hybrid “Box–Jenkins” system with multiple unknown time delays from sampled data. The proposed technique allows the division of the global CT hybrid “Box–Jenkins” system into two fictitious subsystems: the first one contains the parameters of the system model, including the multiple unknown time delays, and the second contains the parameters of the noise model. Then the TS-RLS identification algorithm can be applied easily to estimate all the parameters of the studied system.

The purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.

Computation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.

In this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.

Presented methods are a new way for computing the solution of singular 2D hybrid linear systems.

Complexity is worth studying as a subject for its own sake. We intend to investigate complexity in the context of a fairly broad class of dynamical systems (known as sequential machines). A sequential machine is a perfectly good model of an organization (or organism) which strives for survival, acting under resource and time constraints. For a given complexity level of the system design we could find the level of contact indicating—roughly—the level of understanding of the system transformation. We call this the control complexity. The “information technology” is generated by the lattice of partitions of the state space of the system realized by a serial‐parallel decomposition into component systems.

The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling method, the analysis of the transient and the steady states of the buck dc‐dc converter can be performed.

The proposed method is based on the two Laplace and Z transforms. In the proposed method, at first, the equations of the inductor current and the capacitor voltage are obtained as the power switch is on and off. Then by using the Laplace and Z transforms, the obtained equations are solved and the relations of the inductor current and the output voltage are obtained. In the proposed method, the Laplace transform is used for determining of the general relations of the inductor current and the output voltage. Also the Z‐transform is used as a tool for determining the initial values of the inductor current and the output voltage.

The transient and the steady state response of the dc‐dc converter is analyzed by the proposed method. By using the Z‐transform, the transient response of the converter and the effect of the elements of the converter on the time constant of the transient response are investigated. In addition, the effect of the elements of the converter and the load resistance on the electrical parameters of the converter such as the output voltage ripple and the inductor current ripple are investigated.

The proposed method in this paper is a suitable method for mathematical modeling of dc‐dc converters. The acernote of this method is that it can be used in both transient and steady state response, analysis of the dc‐dc converters. By using the final value theorem of the Z‐transform, the steady state response of the converter is investigated. Also by using this transform, the time constants of the transient response of the converter are determined. Finally, the results of the theoretical analysis are compared with the results of simulation in PSCAD/EMTDC and also the experimental results to prove the validity of the presented subjects.

The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.

The purpose of this paper is to develop a dual peg-in-hole insertion strategy. Dual peg-in-hole insertion is the most common task in manufacturing. Most of the previous work develop the insertion strategy in a two- or three-dimensional space, in which they suppose the initial yaw angle is zero and only concern the roll and pitch angles. However, in some case, the yaw angle could not be ignored due to the pose uncertainty of the peg on the gripper. Therefore, there is a need to design the insertion strategy in a higher-dimensional configuration space.

In this paper, the authors handle the insertion problem by converting it into several sub-problems based on the attractive region formed by the constraints. The existence of the attractive region in the high-dimensional configuration space is first discussed. Then, the construction of the high-dimensional attractive region with its sub-attractive region in the low-dimensional space is proposed. Therefore, the robotic insertion strategy can be designed in the subspace to eliminate some uncertainties between the dual pegs and dual holes.

Dual peg-in-hole insertion is realized without using of force sensors. The proposed strategy is also used to demonstrate the precision dual peg-in-hole insertion, where the clearance between the dual-peg and dual-hole is about 0.02 mm.

The sensor-less insertion strategy will not increase the cost of the assembly system and also can be used in the dual peg-in-hole insertion.

The theoretical and experimental analyses for dual peg-in-hole insertion are proposed without using of force sensor.

The dynamic measure of risk problem in a incomplete market is discussed when stock appreciation rates are uncertain. Meanwhile, a related stochastic game problem is studied. The value of a stochastic optimal control is regarded as a reasonable measure of the risk. The form of the optimal objective is obtained by employing the tools of BSDE theory.

To provide an overview of how a number of frequently used smoothing‐based forecasting techniques can be modelled for use in dynamic analysis of production‐inventory systems.

The smoothing techniques are modelled using transfer functions and state space representation. Basic control theory is used for analysing the dynamic properties.

A set of expressions are derived for the smoothing techniques and dynamic properties are identified.

Dynamic properties are important in many applications. It is shown that the different smoothing techniques can have very different influences on the dynamic behaviour and therefore should be considered as a factor when smoothing parameters are decided on.

Dynamic behaviour of production‐inventory systems can be analysed using control theory based on, e.g. transfer functions or state space models. In this paper a set of models for five common smoothing techniques are analysed and their respective dynamic properties are highlighted.

The purpose of this paper is to improve the transient response and the inter‐sample behavior of a model reference adaptive control system by an appropriate selection of the fractional order hold (FROH) gain β and the multirate gains used in the control reconstruction signal through a fully freely chosen reference model even when the continuous plant possesses unstable zeros.

A multiestimation adaptive control scheme for linear time‐invariant continuous‐time plant with unknown parameters is presented. The set of discrete adaptive models is calculated from a different combination of the correcting gain β in a FROH and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. Then the scheme selects online the model with the best continuous‐time tracking performance which includes a measure of the inter‐sample ripple, which is improved. The estimated discrete unstable zeros are avoided through an appropriate design of the multirate gains so that the reference model might be freely chosen with no constraints on potential unstable zeros.

The scheme is able to select online the discretization model with the best continuous‐time tracking performance without an appropriate initialization.

The switching mechanism among the different models should maintain in operation the active discretization model at least for a minimum residence time in order to guarantee closed‐loop stability. The inter‐sample behavior is improved, but it is not always completely removed.

The transient response and the inter‐sample behavior are improved by using this multiestimation‐based discrete controller compared with a single estimation‐based one. The implementation of discrete controllers makes it easier and cheaper to implement and also more reliable than continuous‐time controllers.

The main innovation of the paper compared with previous background work is that the reference output is supplied by a stable continuous transfer function. Then the scheme is able to partly regulate the continuous‐time tracking error while the controller is essentially discrete‐time and operated by a FROH in general.